# Signal Development for Saturated Ultrafast Sensors with Impact Ionization Gain

## TL;DR

This paper derives an approximate expression for the initial signal development in ultrafast silicon diode sensors, comparing LGAD and PIN types, and discusses their performance limits at extremely high frame rates.

## Contribution

It introduces a closed-form expression for the early-time signal development in silicon diode sensors, including gain effects, and analyzes their performance at gigahertz frame rates.

## Key findings

- LGAD sensors with gain of 30 outperform PIN diodes at up to 10 GHz frame rate.
- The derived expression captures the initial signal rise in high-speed X-ray detection.
- Impact ionization gain extends the effective detection rate for silicon sensors.

## Abstract

A closed-form approximate expression is presented for the short time-frame development of silicon diode sensor signals in the context of high frame-rate detection of incident X-ray fluxes, in the limit that the X-ray absorption profile generates a longitudinally-uniform distribution of electron-hole pairs in the detector bulk. The expression represents the immediate time development of signals from diode sensors both with (LGAD) and without (PIN) gain, and presents a temporal scale associated with the onset of gain. Principles limiting the detection frame rate in the presence of electronic readout noise are discussed. Making use of an elemental simulation, the relative advantage of LGAD vs. PIN diode sensors is explored as a function of the effective electronic collection time. It is found that for an idealized LGAD sensor with a gain of 30, the gain provided by impact ionization yields an advantage relative to PIN diode sensors for frame rates as high as 10 GHz.

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Source: https://tomesphere.com/paper/1908.04953